### Home > CALC > Chapter 10 > Lesson 10.1.7 > Problem 10-66

By now you are comfortable with the graphical implications of the first and second derivatives of a function. gives you the slope of the tangent while

*tells you the concavity of the graph at a point. There is nothing to stop us from finding the third and fourth (and beyond!) derivatives, but there are not any significant graphical characteristics associated with higher derivatives.*

*is simply the rate of change of*

*and so on.*

Notation: We cannot simply put more and more tic marks for, say, the 7 , using italicized roman numerals. The ^{th} derivative of a function is written . |

Find

for.Take the derivative four times.

If

^{ }, find an expression for the^{th}derivative,.Take a few derivatives of this function and look for patterns.